Abstract : In this article, we introduce a Riemann solver for traffic flow on a roundabout with two lanes. The roundabout is modeled as a sequence of 2 × 1, 1 × 2 and 2 × 2 junctions. The Riemann solver provide a solution at junctions by taking into consideration traffic distribution, priorities, and the maximization of through flux. We prove existence and uniqueness of the solution of the Riemann problem and show some results numerically.